= 4. Consider a D/M/1 queue, where arrivals occur every minute. Assuming the system starts empty...

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= 4. Consider a D/M/1 queue, where arrivals occur every minute. Assuming the system starts empty (first arrival at time t 1 minute), we wish to estimate the probability that a customer has to wait. To simplify things, we will consider only the second customer. For a mean service time of 1 second, estimate the probability based on 1000 replications (a) using straightforward simulation (b) using simulation via importance sampling with mean service time of 1 minutes (c) using exactly analytical calculation. (d) explain how you would carry out (b) over all customers (instead of just the second). = 4. Consider a D/M/1 queue, where arrivals occur every minute. Assuming the system starts empty (first arrival at time t 1 minute), we wish to estimate the probability that a customer has to wait. To simplify things, we will consider only the second customer. For a mean service time of 1 second, estimate the probability based on 1000 replications (a) using straightforward simulation (b) using simulation via importance sampling with mean service time of 1 minutes (c) using exactly analytical calculation. (d) explain how you would carry out (b) over all customers (instead of just the second).